A244878 Number of 6 X 6 traceless symmetric magic squares with magic sum n.

1, 15, 130, 760, 3355, 12043, 36935, 100135, 245870, 556580, 1177295, 2351165, 4469610, 8141210, 14284170, 24247962, 39970575, 64178685, 100639000, 154470030, 232524589, 343854445, 500269705, 717006745, 1013519780, 1414412506, 1950527645, 2660213675, 3590789540, 4800229700

Offset: 0

Author

N. J. A. Sloane, Jul 08 2014

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]
• Index entries for linear recurrences with constant coefficients, signature (9,-35,75,-90,42,42,-90,75,-35,9,-1).

Crossrefs

Row n=6 of A333351.

Programs

Mathematica

LinearRecurrence[{9,-35,75,-90,42,42,-90,75,-35,9,-1},{1,15,130,760,3355,12043,36935,100135,245870,556580,1177295},30] (* Harvey P. Dale, Jul 18 2024 *)

PARI

Vec((1 + 6*x + 30*x^2 + 40*x^3 + 30*x^4 + 6*x^5 + x^6) / ((1 - x)^10*(1 + x)) + O(x^30)) \\ Colin Barker, Jan 12 2017

Formula

G.f.: (1 + 6*x + 30*x^2 + 40*x^3 + 30*x^4 + 6*x^5 + x^6) / ((1 - x)^10*(1 + x)).

a(n) = (945*(507+5*(-1)^n) + 1480896*n + 2062800*n^2 + 1747040*n^3 + 989100*n^4 + 383628*n^5 + 100800*n^6 + 17160*n^7 + 1710*n^8 + 76*n^9) / 483840. - Colin Barker, Jan 12 2017